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I have a EEG data of epileptic patients. I have applied two different approaches for feature generation i.e Discrete Wavelet Transform (DWT) and Dual Tree Complex Wavelet Tranform(DTCWT). I have found better results with DTCWT. To support my approach , I want to show that DWT is shift variant but DTCWT do not get much affected by shift. I have searched alot but could not find a proper way of comparing the shift variance of both dwt and dtcwt in python. Can someone help me?

anonymous
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  • If this is an exclusive Python question, please remove the matlab tag. If not, please provide some clues to justify the tag. In general, show your relevant code in terms of a [mre], and what have you tried so far regarding your problem, i.e. extracting information about the shift (in)variance of both WTs. – HansHirse Jun 21 '19 at 06:24
  • Actually I have gone through various texts and realised that for demonstration purpose, I will have to construct two shifted discrete-time impulses and maybe then compute the energy (squared norms) of the coefficients. But how do I do this? my dataset have 100 features. so should I take data from index 1 to 90 and other from 11 to 100? – anonymous Jun 21 '19 at 08:05
  • How many levels of the DWT do you use? The one-level DWT is shift-invariant if you shift a signal by even number of samples, the two-level DWT is invariant for four-sample shifts, the three-level DWT for 8-sample shifts, etc. On the other hand, the DTCWT is shift-invariant for any whole-sample shift (but not for half-sample shifts, etc.) – DaBler Jan 18 '20 at 09:43

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